Sorry, I don't understand what baby rice is, may you can explain it to me? xD
A hamster is not allowed to get milk, because all little mammals have an lactose intolerance. At least in germany we said so. Milk is not very good.
If you want to give him something good and special, or to make him a little stronger if he's ill, then i would prefer baby porridge in glasses. Especially the vegetables porridges! My hamsters loved it